Factors

FACTORS

What numbers can multiply up to make

24 ? 1 , 24 4 , 6 2 , 12 3 , 8

These are all FACTORS of 24

PRIME NUMBERS: Numbers that don’t have any factors except 1 and itself. 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, etc…

In other words, PRIME NUMBERS can’t be divided evenly by anything except themselves.

Class Work paper Are these numbers Prime or “Composite” (not Prime)? Yes or No? 1. 13 2. 50 3. 119 4. 11 5. 121

PRIME FACTORS

You can divide up any number into it’s Prime Factors using a “Factor Tree”. Example: Find the PRIME FACTORS of the number 36.

36

6 • 6

What two numbers multiply to make Are 36?these numbers prime, or can we divide them up more?

2•3•2•3

ALL PRIME FACTORS OF 36

Prime Factors 24 = 2 • 12 =2•2•6 =2•2•2•3 50 = 2 • 25 =2•5•5

It doesn’t matter how you divide them up, you still get the same result!

same thing !

= 5 • 10 =5•2•5

When finding the prime factors of monomials, just write out all the letters at the end. EXAMPLE: Find the Prime Factors of:

32x2y4 2 4 = 8•4•x •y = 2 • 4 • 2 • 2 • x2 • y4 = 2•2•2•2•2•x•x•y•y•y•y

To find the prime factors of a NEGATIVE NUMBER, just factor out a -1 EXAMPLE: Find the Prime Factors of: -12a2b4

= -1 • 12 • a2 • b4 = -1 • 2 • 6 • a2 • b4 = -1 • 2 • 2 • 3 • a • a • b • b • b • b

GREATEST COMMON FACTOR

“Biggest” “Same” “Number that divides perfectly”

Find the Greatest Common Factor of the two numbers given:

25: 1, 25, 5, 5, 36: 1, 36, 2, 18, 3, 12, 4, 9, 6, 6, What is the highest factor they both have the same?

What are all the factors of each? The GCF of 25 & 36 is 1

What is the GCF of 100 & 60 ?

100: 1, 100, 2, 50, 4, 25, 5, 20, 10, 10 60: 1, 60, 2, 30, 3, 20, 4, 15, 5, 12, 6, 10

The GCF of 100 & 60 is 20.